Timeline for Algebraic topology beyond the basics: any texts bridging the gap?
Current License: CC BY-SA 2.5
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| Dec 27, 2011 at 20:17 | history | made wiki | Post Made Community Wiki by François G. Dorais | ||
| Mar 14, 2010 at 14:16 | comment | added | Tim Perutz | @Tim Porter (and Robin Chapman). - Interesting; I'd assumed that Adams's book is redundant, apart from its introduction, if one can download those papers. Perhaps I neglected the psychological difficulty of leaving textbooks behind. I wonder if the "classic paper" approach is also viable for the Age of Big Algebraic Machines in algebraic topology - I mean post Quillen's work on MU! An obvious difficulty is that it took 30-odd years for the definition of the category of spectra to stabilise. | |
| Mar 14, 2010 at 7:13 | comment | added | Tim Porter | Perhaps another question to ask is how should the student in algebraic topology, be best helped to make the transition mentioned. | |
| Mar 14, 2010 at 7:13 | comment | added | Tim Porter | I have always found Frank Adams book mentioned above to be very useful for students (and self). It acts as a bridge to the student attacking the source material in the journals. One or more similar collections would be useful for future developments, but I feel that Alg Top is much too big now to be contained adequately in a single text. Look at the Handbook of Algebraic Topology, which has some survey articles in (edited some years ago buy Ioan James). It provides a multitude of ideas for students but it is not a textbook. | |
| Mar 13, 2010 at 22:22 | comment | added | The Mathemagician | I hope to be taking Dennis Sullivan's advanced topology course and string theory seminar at The City University Of New York Graduate Center next year while my PHD program applications are processed.I'm hoping that will not only expose me to the cutting edge,but allow me to work with one of the greats. | |
| Mar 13, 2010 at 21:58 | comment | added | Robin Chapman | Frank Adams's book "Algebraic topology: a student's guide" is a collection of such classic papers. | |
| Mar 13, 2010 at 21:30 | comment | added | Steven Sivek | The Kan seminar (18.915) at MIT does exactly this every fall -- see www-math.mit.edu/~mbehrens/18.915/index.html for two lists of suggested papers. | |
| Mar 13, 2010 at 21:12 | history | answered | Tim Perutz | CC BY-SA 2.5 |